1. Field
Embodiments of the present invention relate to system testing and more particularly to testing radio frequency (RF) signals in computer systems and telecommunication systems.
2. Background Information
Timing, frequency, and phase measurements in high-frequency (e.g., radio frequency (RF)) systems such as computer systems and telecommunication systems have received much attention in recent years. Measuring parameters in these systems, which have clocks and data transmission rates in the gigahertz (GHz) range, has proven challenging, however. Nonetheless, accurate estimation of parameters such as signal period, frequency, phase, jitter, edges rates (rise and fall times), etc., is essential for designing such systems as well as for characterizing their operation.
Traditional measurement techniques include bit-error-rate (BER) tests or jitter tests, which are used to characterize errors in the received data of serial data bit streams. BER testing is limited, however, in that it tends to be time consuming and it does not characterize phase variations or frequency variations in the serial data stream during the telecommunication system design stage as well as during operation.
Another technique is the omnipotent fast Fourier transform (FFT) whose implementation provides full signal information in both the amplitude and phase spectra. Clever techniques have been devised to extract specific timing and phase characteristics (e.g., jitter, phase noise) by processing these spectra. The FFT, however, has a critical shortcoming for these specific applications. It loses all time information in the transform computation of the spectra. A frequency change or phase change may be detected in a signal, but the user does not know when the change took place.
This can be particularly troublesome when frequency-hopping techniques called for by wireless telecommunication standards are used to find a possible available channel. In the frequency-hopping case, the FFT spectrum shows several carrier frequencies, but does not show the time windows corresponding to each carrier frequency. Additionally, the FFT computational process can be rather slow.
The Hilbert transform is an alternative technique that may be used to estimate phase and jitter. The Hilbert transform also loses all time information in the transform computation of the spectra, however, and thus is not suitable for estimating phase.
A joint-time frequency analysis using the short-time FFT (SFFT) and a continuous Gaussian-derived wavelet retains time information in the transform computation. Its application requires a large number of samples in each time window to compute the spectrum using the basic FFT algorithm, however.